Oberseminar Wahrscheinlichkeitstheorie und andere Vorträge im Sommersemester 2022

Organisers: Nina Gantert (TUM), Noam Berger (TUM), Markus Heydenreich (LMU), Franz Merkl (LMU), Silke Rolles (TUM), Konstantinos Panagiotou (LMU), Sabine Jansen (LMU),

Talks:

Monday, 25th April 2022, 16:30, (using zoom)
Gideon Chiusole (TUM)
Title: A Brief Introduction to Rough Paths
Abstract: Rough Paths are a suitable generalization of smooth paths in settings where classical (Riemann-Stieltjes, Young, ...) integration breaks down, most notably for integral formulations of (stochastic/controlled) differential equations. We'll give a short account of the key objects, spaces, properties involved, as well as some subtleties of the theory. The focus of the talk is going to be on the motivation via the "Rough Path principle" and rough integration as well as on "the big picture".

Monday, 2th May 2022, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Sarai Hernandez-Torres (Technion, Haifa)
Title: The chemical distance in random interlacements in the low-intensity regime
Abstract: Random interlacements is a Poissonian soup of doubly-infinite random walk trajectories on Z^d, with a parameter u > 0 controlling the intensity of the Poisson point process. In a natural way, the model defines a percolation on the edges of Z^d with long-range correlations. We consider the time constant associated to the chemical distance in random interlacements at low intensity u > 0. It is conjectured that the time constant times u^{1/2} converges to the Euclidean norm, as u ↓ 0. In dimensions d ≥ 5, we prove a sharp upper bound and an almost sharp lower bound for the time constant as the intensity decays to zero. Joint work with Eviatar Procaccia and Ron Rosenthal.

Monday, 23th May 2022, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Pierre Tarres (TUM)
Title: *-Edge-reinforced random walk and *-vertex-reinforced jump processes: limit measure and random Schrödinger representation
Abstract: TBA

Monday, 4th July 2022, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Simone Floreani (TU Delft)
Title: Hydrodynamics for the partial exclusion process in random environment
Abstract: In this talk, I present a partial exclusion process in random environment, a system of random walks where the random environment is obtained by assigning a maximal occupancy to each site of the Euclidean lattice. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we prove that the quenched hydrodynamic limit is a heat equation with a homogenized diffusion matrix. The first part of the talk is based on a joint work with Frank Redig (TU Delft) and Federico Sau (IST Austria).Finally, I will discuss some recent progresses in the understanding of what happens when removing the uniform ellipticity assumption. After recalling some results on the Bouchaud’s trap model, I will show that, when assuming that the maximal occupancies are heavy tailed and i.i.d., the hydrodynamic limit is the fractional-kinetics equation.The second part of the talk is based on an ongoing project with Alberto Chiarini (University of Padova) and Frank Redig (TU Delft).

Monday, 11th July 2022, 15:00, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Thomas Richthammer (Universität Paderborn)
Title: Spatial Monotonicity Properties of Bernoulli Percolation
Abstract: We consider Bernoulli percolation on a graph G =(V,E). Interpreting some chosen reference vertex o in V as the origin of an infection, the percolation cluster of o corresponds to the set of all infected vertices.  It is very natural to expect that the probability for a vertex v in V to be infected should (in some sense) be decreasing in the distance of v to o. One possible rigorous formulation of this property is the famous bunkbed conjecture, which dates back to the 80s and still remains wide open. It seems that this kind of spatial monotonicity property of percolation in general is difficult to obtain. Here we present several new results relying on symmetry considerations or a Markov chain approach. Some of these results are joint work with Philipp König.
Im Anschluss daran:
Monday, 11th July 2022, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Olga Aryasova (Universität Jena)
Title: TBA

Monday, 18th July 2022, 16:30, LMU, room B252, Theresienstr. 39, Munich
Ruizhe Sun (LMU)
Title: Epidemics on Random Intersection Graphs
Abstract: In this thesis, we develop a Reed-Frost model based on random intersection
graphs. Our interest is the size of the set of ultimately recovered individuals as
population size grows to infinity. Several branching processes will be constructed
as approximating processes to serve this purpose. Eventually, benefiting from
the clique-based structure provided by the random intersection graph, we will
discuss the exact distribution of the quantity of interest in both small and large
outbreaks.

Monday, 25th July 2022, 16:30, TUM, room 2.01.10, Parkring 11, Garching-Hochbrück (Technische Universität München)
Viktor Bezborodov (Universität Göttingen)
Title: TBA

 

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